60 terms

Slope

y2-y1/x2-x1; horizontal lines:zero slope:y=b; vertical lines:undefined/infinite slope:x=a

Lines of Fit

Equal number of points above and below the line; line follows the trend in the data points

Point Slope Form

(y1-y2)=m(x1-x2); known slope m, unknown point (x1, y1), unknown point (x,y); move the denominator over to the other side

Equivalent Expression

Two expressions that look different but have the same math value; converting between point-slope and slope-intercept forms of a line

System of Equations

Two or more equations that have the same variables; one solution, all solutions, or no solutions

Solutions

A single point in which works in both equations

Solve Using Substitution

Solve one equation for a variable; plug that equation into the other equation; solve for the unknown; plug back into he starting equations to find the other unknown

Solve Using Elimination

Add two equations together so that one variable will cancel out; this may require modifying the equation first by multiplying through by a constant; solve the resulting one-variable equation; plug back into the original equation to get the second value of the solution point

Inequalities in One Variable

Treat the inequality like an equal sign when you do the math to both sides; if you multiply/divide by a negative, FLIP the direction of the inequality; open or closed circle when graphing

Inequalities in Two Variables

Graph the line like normal, then figure out if it is dotted or solid: solid lines if the line is included, dotted lines if the line is not included; now figure out were to shade: above the line if greater than, below the line if less than; graph on the

Graphing Systems of Inequalities

Graph both inequalities on the same axis; where they overlap is the solution; plug a point into both equations to check

Relation

Any relationship between two variables (aka not random)

Function

A relation that has exactly one output for each input

Domain

All possible input values (x)

Range

All possible output values (y)

Vertical Line Test

If a vertical line crosses a graph more than once, then the graph is not a function. If it crosses only once, then the graph is a function.

Counterexample

An example that proves an idea wrong by contradicting it

Linear

Graph is a straight line

Non-Linear

Graph is curvy (there are many types)

Independent Variable

Input; horizontal axis; (usually) x-axis

Dependent Variable

Output; vertical axis; (usually) y-axis; depends on input value

Increasing Functions

As input gets larger, output also get larger (positive slope)

Decreasing Functions

As input gets larger, output get smaller (negative slope)

Continuous Function

No breaks in domain or range

Discreet (Discontinuous) Function

Has gaps or breaks (often for quantified data)

f(x)

'f' is the name of the function and the output variable. 'x' is the input variable; f(3) means plug in for x and then get out the answer

Translating Points

xnew=xold+deltax (side to side); ynew=yold+deltay (up and down)

Translating Graphs

Up k, (y), (y-k); down k, (y), (y+k); right h, (x), (x-h); left k, (x), (x+h); for up and right you subtract, for down and left you add; (y-k)=f(x-h)

Reflecting Points and Graphs

Flip across y-axis, x -> -x; flip across x-axis, y -> -y

Stretching and Shrinking Graphs

To stretch multiply the entire function by a number larger than 1; to shrink multiply the entire function by a number smaller than 1; stretching and shrinking in the vertical direction never changes the x-intercepts

Asymptote

A straight line that the graph approaches but does not cross

Polynomial

A sum of terms with only positive exponents

Rational Function

A ratio of two polynomials; denominator cannot be zero

Inverse Variation Function

y=k/x (be able to graph and shift this)

Common Denominators

Adding or subtracting fractions that have identical denominators. You need to get a common denominator before combining

Butterfly Technique

Breaking a rational function into separate pieces by writing each part of the numerator over the denominator separately, then simplifying

General/Standard Form

y=ax2+bx+c=0; c=y intercept

Vertex Form

(y-k)=a(x-h)2; (h,k)=vertex

Factored Form

y=a(x-r1)(x-r2); r1, r2=roots

Roots

Where the graph crosses the x-axis

Zeroes

Same as roots

X-Intercepts

Same as roots

Y-Intercepts

Where the graph crosses the y-axis

Vertex

The "center point" that divides the parabola into two symmetrical halves

Quadratic Equation

The equation with x2 as the highest degree

Parabola

The graph for a quadratic equation

Perfect Squares

(x+n)2=x2+2nx+n2; square root of a negative=no solution

Volume of a cube

(length)(width)(height), but all of them are the same distance, call it x; V=(x)(x)(x)=x3; for side length take the 'cube root,' x=cuberootV=V1/3

Parallel

Two lines with the same slope

Perpendicular

Two lines that cross at a right angle; the slope of the lines are the negative reciprocal of each other; the product of the slopes is -1

Reciprocal

Flip the fraction over

Midpoint

A point halfway between two other points; (x1+x2/2, y1+y2/2); to find the median of a triangle, the line from a vertex to the opposite midpoint; to find the perpendicular bisector, a line that is perpendicular to and contains the midpoint of another line

Pythagorean Theorem

For a right triangle with legs a, b, and hypotenuse c; a2+b2=c

Similar Triangles

Triangles in which the angles and the ratio of the sides are the same

Distance Formula

d=squareroot (x2-y1)^2+(y2-y1)^2; to remember, draw a triangle and apply the pythagorean theorem

Quadratic Formula (Roots and Factored Form)

x=-b+or-squareroot b^2-4ac/2a; b^2-4ac is called the "discriminant" and tells you how many answers there will be; if positive -> two answers; if zero -> one answer; if negative -> no answers

Factor by Hand (Factored Form)

Find two numbers that multiply to 'c' and add to 'b'

FOIL (General Form)

Multiply the terms corresponding to FOIL, then add them up, combining like terms. Follow PEMDAS

Converting to Vertex Form

xvertex=-b/2a (from general form) ; xvertex=halfway between the roots (from factored form)

Complete the Square

y=(x^2+vx+__)-__ ->y=x^2+bx_(b/2)^2-(b/2)^2 -> y=(x+b/2)^2-(b/2)^2; if the leading coefficient is not a 1,you should factor it out from all the terms before you start completing the square